We consider the following problem: the UAV, which is at its origin \(O\) , is supposed to move to its destination \(A\)  as early as possible, in which the path length \(|OA|=a\) . The UAV has a low charging rate \(\alpha \)  per unit time and a high power-consuming rate \(\beta \)  (\(>\alpha \) ) per unit time. Initially at time 0, the UAV stores an amount \(P_0\)  of energy (which is small and could be zero) and it flies at its maximum velocity
In practice, the UAV can convert its speed between 0 and its maximum speed in few seconds [1]}. Considering the dominant travel time, we assume the flying velocity as a constant as in [2]}, [1]}. \(v_0\) . To avoid the trivial case that the UAV directly flies to the destination by charging on the way, we assume the UAV has insufficient energy \(P_0\)  (\(<\frac{(\beta -\alpha )a }{v_0}\) ). That is, the UAV needs to hitch truck rides to save flying distance or charge for sufficiently large amount of time to fly to the destination. Along the path \(OA\)  of the UAV, a sequence \(\mathbb {V}=\lbrace V_1, V_2,..., V_n\rbrace \)  of \(n\in \mathbb {N}^+\)  trucks will be released one by one to potentially offer rides to the UAV. Each truck \(V_i=(r_i,t_i,o_i,d_i,v_i)\in \mathbb {V}\)  releases its trip information to the UAV at time \(r_i\)  and departs from its origin \(o_i\)  at time \(t_i\)  (\(\ge r_i\) ) with a constant velocity \(v_i\)  to its destination \(d_i\) . Further, we denote \(\Delta t_i=t_i-r_i\)  as the time gap between the start time \(t_i\)  and the release time \(r_i\)  of a truck ride \(V_i\) . The UAV is not informed of each ride \(V_i\in \mathbb {V}\)  until its release time \(r_i\)  (when the truck's schedule is determined) and needs to determine whether to accept/catch or reject \(V_i\)  irrevocably at \(r_i\) . The objective is to minimize the UAV's travel time to the destination \(A\)  (or equivalent, the arrival time at \(A\) ) by using online truck rides to save energy halfway. Key notations of this paper are given below in Table REF .
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